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    }
   },
   "source": [
    "# Self-Attention and Positional Encoding\n",
    "\n"
   ]
  },
  {
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   "source": [
    "import math\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ee3522",
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    "Self-Attention"
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   "source": [
    "num_hiddens, num_heads = 100, 5\n",
    "attention = d2l.MultiHeadAttention(num_hiddens, num_heads, 0.5)\n",
    "batch_size, num_queries, valid_lens = 2, 4, torch.tensor([3, 2])\n",
    "X = torch.ones((batch_size, num_queries, num_hiddens))\n",
    "d2l.check_shape(attention(X, X, X, valid_lens),\n",
    "                (batch_size, num_queries, num_hiddens))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "525745e4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "Positional Encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3eb1b5ef",
   "metadata": {
    "execution": {
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   "source": [
    "class PositionalEncoding(nn.Module):  \n",
    "    \"\"\"Positional encoding.\"\"\"\n",
    "    def __init__(self, num_hiddens, dropout, max_len=1000):\n",
    "        super().__init__()\n",
    "        self.dropout = nn.Dropout(dropout)\n",
    "        self.P = torch.zeros((1, max_len, num_hiddens))\n",
    "        X = torch.arange(max_len, dtype=torch.float32).reshape(\n",
    "            -1, 1) / torch.pow(10000, torch.arange(\n",
    "            0, num_hiddens, 2, dtype=torch.float32) / num_hiddens)\n",
    "        self.P[:, :, 0::2] = torch.sin(X)\n",
    "        self.P[:, :, 1::2] = torch.cos(X)\n",
    "\n",
    "    def forward(self, X):\n",
    "        X = X + self.P[:, :X.shape[1], :].to(X.device)\n",
    "        return self.dropout(X)"
   ]
  },
  {
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   "id": "a0548d5d",
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   "source": [
    "Rows correspond to positions within a sequence\n",
    "and columns represent different positional encoding dimensions"
   ]
  },
  {
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   "execution_count": 4,
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    "encoding_dim, num_steps = 32, 60\n",
    "pos_encoding = PositionalEncoding(encoding_dim, 0)\n",
    "X = pos_encoding(torch.zeros((1, num_steps, encoding_dim)))\n",
    "P = pos_encoding.P[:, :X.shape[1], :]\n",
    "d2l.plot(torch.arange(num_steps), P[0, :, 6:10].T, xlabel='Row (position)',\n",
    "         figsize=(6, 2.5), legend=[\"Col %d\" % d for d in torch.arange(6, 10)])"
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   "source": [
    "The binary representations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6f42d89b",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2023-08-18T19:30:36.378862Z"
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     "pytorch"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 in binary is 000\n",
      "1 in binary is 001\n",
      "2 in binary is 010\n",
      "3 in binary is 011\n",
      "4 in binary is 100\n",
      "5 in binary is 101\n",
      "6 in binary is 110\n",
      "7 in binary is 111\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(f'{i} in binary is {i:>03b}')"
   ]
  },
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   "cell_type": "markdown",
   "id": "e137cf32",
   "metadata": {
    "slideshow": {
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   "source": [
    "The positional encoding decreases\n",
    "frequencies along the encoding dimension"
   ]
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     "pytorch"
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